# Right Prism: Surface Area

How to find the surface area of a right prism: definition, formula, 2 examples, and their solutions.

## Prism

### Definition

A prism is a 3D figure

that has

a pair of polygon bases

and quadrilateral lateral faces.

The bases are congruent and parallel.

## Right Prism

### Definition

A right prism is a prism

whose lateral faces are all rectangles

and are perpendicular to the bases.

## Formula

### Formula

A = 2B + Ph

A: Surface area of a right prism

B: Base area

P: Perimeter of the base

h: Height

2B is the two base areas.

Ph is the lateral area.

## Example 1

### Example

### Solution

Find the base area B.

The base is a rectangle.

Its sides are 7 and 5.

So the area of the rectangle is

B = 7⋅5.

7⋅5 = 35

So the base area B is 35.

Find the perimeter of the base P.

The base is a rectangle.

So its sides are 7, 5, 7, and 5.

So the perimeter P is 2(7 + 5).

7 + 5 = 12

2⋅12 = 24

So the perimeter of the base P is 24.

The height h is 8.

B = 35

P = 24

h = 8

Then the surface area A

is equal to,

two base areas 2B, 2⋅35

plus,

the lateral area Ph, 24⋅8.

So A = 2⋅35 + 24⋅8.

2⋅35 = 70

+24⋅8 = +192

70 + 192 = 262

So the surface area of the right prism is

262.

## Example 2

### Example

### Solution

Find the base area B.

The base is an equilateral triangle.

Its side is 4.

So the area of the equilateral triangle is

B = [√3/4]⋅4^{2}.

[√3/4]⋅4^{2}

= √3⋅4

= 4√3

So the base area B is 4√3.

Find the perimeter of the base P.

The base is an equilateral triangle.

So its sides are 4, 4, and 4.

So the perimeter P is 3⋅4.

3⋅4 = 12

So the perimeter of the base P is 12.

The height h is 7.

B = 4√3

P = 12

h = 7

Then the surface area A

is equal to,

two base areas 2B, 2⋅4√3

plus,

the lateral area Ph, 12⋅7.

So A = 2⋅4√3 + 12⋅7.

2⋅4√3 = 8√3

+12⋅7 = +84

Arrange the terms.

So the surface area of the right prism is

84 + 8√3.